#include <bits/stdc++.h>
using namespace std;
const long long oo = 1LL << 50;
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, m, s, t, l;
long long k;
cin >> n >> m >> s >> t >> l >> k;
s--; t--;
vector<vector<pair<int, int>>> a(n);
while (m--)
{
int x, y, z;
cin >> x >> y >> z;
a[--x].push_back({--y, z});
a[y].push_back({x, z});
}
auto calcDist = [&](int from)
{
vector<long long> dist(n, oo);
vector<int> flag(n);
dist[from] = 0;
priority_queue<pair<long long, int>> q;
q.push({0, from});
while (!empty(q))
{
auto [_, x] = q.top();
q.pop();
if (flag[x])
continue;
flag[x] = 1;
for (auto [y, w] : a[x])
if (!flag[y] && dist[x] + w < dist[y])
{
dist[y] = dist[x] + w;
q.push({-dist[y], y});
}
}
return dist;
};
auto distS = calcDist(s), distT = calcDist(t);
if (distS[t] <= k)
{
cout << n * (n - 1LL) / 2 << endl;
return 0;
}
vector<int> idS(n);
iota(begin(idS), end(idS), 0);
auto idT = idS;
sort(begin(idS), end(idS), [&](int u, int v) { return distS[u] < distS[v]; });
sort(begin(idT), end(idT), [&](int u, int v) { return distT[u] > distT[v]; });
long long ans = 0;
for (int i = 0, j = 0; i < n && j < n;)
{
int x = idS[i], y = idT[j];
if (distS[x] + distT[y] > k - l) j++;
else
{
ans += n - j;
i++;
}
}
for (int i = 0; i < n; i++)
if (distS[i] + distT[i] <= k - l)
ans--;
cout << ans << endl;
}
